People who ride in hot-air balloons usually fly just above the treetops at 200–500 feet. In populated areas, however, they usually stay at an altitude of at least 1000 feet. The amount of flying time possible in a hot-air balloon depends on many factors, including the number of propane burners, the number of people in the basket, and the weather. Assume the time spent aloft is normally distributed with mean 1.5 hours and standard deviation 0.45 hour. Suppose a hot-air balloon flight is selected at random.
a. What is the probability that the flight time is between 1 and 2 hours?
b. What is the probability that the flight time is more than 1 hour and 15 minutes?
c. Find a value t such that 10% of all flights last less than t hours.
d. Suppose a person offering hot-air balloon rides charges $50 for each ride of at least 1 hour, and $1.00 for every minute after 1 hour. What proportion of rides costs more than $100?
The Daytona 500, often referred to as The Great American Race, is a spectacular sporting event, complete with a pre-race show. Jimmie Johnson won this race in 2013, when the mean speed per lap for all racers was 159.25 mph.13 Assume the speed is normally distributed with a standard deviation of 16 mph, and a driver and lap are selected at random.
a. What is the probability that the speed on this lap is less than 155 mph?
b. What is the probability that the speed on this lap is between 140 and 150 mph?
c. The fastest recorded speed is 212 mph at Talladega in 1986. What is the probability that the speed on this lap will set a new record?
d. What is the probability that the four leaders will all have a speed of at least 165 on this lap?